A173442 Number of divisors d of number n such that sigma(d) does not divide n.

0, 1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 2, 1, 3, 3, 4, 1, 4, 1, 5, 3, 3, 1, 4, 2, 3, 3, 4, 1, 5, 1, 5, 3, 3, 3, 5, 1, 3, 3, 7, 1, 6, 1, 5, 5, 3, 1, 6, 2, 5, 3, 5, 1, 6, 3, 4, 3, 3, 1, 7, 1, 3, 5, 6, 3, 6, 1, 5, 3, 7, 1, 8, 1, 3, 5, 5, 3, 6, 1, 9, 4, 3, 1, 6, 3, 3, 3, 7, 1, 8, 3, 5, 3, 3, 3, 8, 1, 5, 5, 8

Offset: 1

Author

Jaroslav Krizek, Feb 18 2010

Keywords

• nonn

Comments

Sigma(n) = A000203(n). a(n) = A000005(n) - A173441(n).

a(n) >= 1 for n >= 2, with equality if and only if n is prime. - Robert Israel, Oct 10 2017

Examples

			For n = 12, a(12) = 2. We see that the divisors of 12 are 1, 2, 3, 4, 6, 12. The corresponding sigma(d) are 1, 3, 4, 7, 12, 28. The sigma(d) which do not divide n for 2 divisors d are 4 and 12.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000203, A173441.

Programs

Maple

f:= n -> nops(select(t -> n mod numtheory:-sigma(t) <> 0, numtheory:-divisors(n))):
map(f, [$1..100]); # Robert Israel, Oct 10 2017

Mathematica

Table[Length[Select[Divisors[n], Not[Divisible[n, DivisorSigma[1, #]]], &]], {n, 100}] (* Alonso del Arte, Oct 10 2017 *)

PARI

a(n) = sumdiv(n, d, (n % sigma(d)) != 0); \\ Michel Marcus, Oct 11 2017

Extensions

More terms from Robert Israel, Oct 10 2017